Reference request: Chern classes in algebraic geometryI think we're just using different titles for the same thing. Using elementary symmetric polynomials of eigenvalues for a matrix of 2forms to create characteristic classes is very topological but is also called the Chern-Weil approach. Are you thinking of Chern-Simmons maybe?

Improper use of Stokes and Divergence Theorem. Find the problemAs Tunococ said for an open surface the divergence theorem doesn't apply which gives you the problem you were looking for. In the case of a closed surface the argument is valid. Whatever F is if you integrate it over the empty set you're going to get zero.

Going to the Movies!I like this problem. I'm guessing that small independent theaters don't have any sort of algorithm for organizing showtimes to maximize revenue. It seems likely that the google-plexes like AMC do though. If they don't I see some consulting work coming your way soon.

Self-study: part 2700-800 hours was a bit of a wild guess. I think most would agree with me that after that much time you're not going to reach "Fahrenheit 451" status with any of these books. Assuming each hour is undistracted quality time it's possible you could have mostly vanquished the first three and started to make headway on big Rudin.